Subgroups — C₂×C₃×D₅×#92788 #44478159

Order 30420.

960 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#92788	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₅×#92788	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₅×C₁₃²	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅×#92788	C₃	1	3	yes	maximal, direct product factor
5	C₃×C₅×#92788	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂²×C₃×#92788	—	5	1	no	maximal, Hall
7	C₃×D₅×C₁₃²	C₂×C₃	1	2	yes	complemented
8	C₂×C₅×#92788	C₂×C₃	1	3	yes	complemented
9	D₅×#92788	C₂×C₃	1	6	yes	direct product factor
10	C₂×C₃×C₅×C₁₃²	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×D₅×C₁₃²	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×#92788	—	5	2	no	—
13	C₂×C₃×#92788	D₅	1	1	yes	characteristic, direct product factor
14	C₅×#92788	C₂²×C₃	1	3	yes	complemented
15	C₃×C₅×C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃×D₅×C₁₃⋊C₃	—	13	14	no	maximal
17	C₂²×#92788	—	5	3	no	—
18	C₂²×C₃×C₁₃²	—	5	1	no	—
19	C₂×C₅×C₁₃²	C₂×C₃²	1	1	yes	characteristic, complemented
20	D₅×C₁₃²	C₂×C₃²	1	2	yes	complemented
21	C₃×#92788	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₅×C₁₃⋊C₃	—	13	14	no	—
23	C₃×D₅×C₁₃⋊C₃	—	13	28	no	—
24	C₂×C₃×C₁₃²	—	5	2	no	—
25	C₂×C₃×C₁₃²	C₃×D₅	1	1	yes	characteristic, complemented
26	C₂×#92788	—	5	6	no	—
27	C₂×#92788	C₃×D₅	1	3	yes	direct product factor
28	C₅×C₁₃²	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×D₅×C₁₃	C₁₃⋊C₃	1	14	yes	complemented
30	C₂×D₅×C₁₃⋊C₃	—	13	42	no	—
31	C₂²×C₁₃²	—	5	1	no	Hall
32	C₃×C₅×C₁₃⋊C₃	—	13	14	no	—
33	C₃×C₁₃²	C₂×C₃×D₅	1	1	yes	characteristic, complemented
34	#92788	C₂×C₃×D₅	1	3	yes	direct product factor
35	C₂²×C₃×C₁₃⋊C₃	—	65	14	no	—
36	C₂×C₃×C₅×C₁₃	C₂×C₁₃⋊C₃	1	14	yes	complemented
37	C₃×D₅×C₁₃	C₂×C₁₃⋊C₃	1	28	yes	complemented
38	C₂×C₅×C₁₃⋊C₃	—	13	42	no	—
39	D₅×C₁₃⋊C₃	—	13	84	no	—
40	C₂×C₁₃²	—	5	2	no	—
41	C₂×C₁₃²	C₃²×D₅	1	1	yes	characteristic, complemented
42	C₂×D₅×C₁₃	C₃×C₁₃⋊C₃	1	14	yes	complemented
43	C₂×C₃×C₁₃⋊C₃	—	13	14	no	—
44	C₂×C₃×C₁₃⋊C₃	—	65	28	no	—
45	C₃×C₅×C₁₃	C₂²×C₁₃⋊C₃	1	14	yes	complemented
46	C₅×C₁₃⋊C₃	—	13	42	no	—
47	C₂×C₃²×D₅	—	169	1	no	Hall
48	C₁₃²	C₂×C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₃×C₁₃	—	5	14	no	—
50	C₂²×C₁₃⋊C₃	—	65	42	no	—
51	C₂×C₅×C₁₃	C₂×C₃×C₁₃⋊C₃	1	14	yes	complemented
52	D₅×C₁₃	C₂×C₃×C₁₃⋊C₃	1	28	yes	complemented
53	C₃×C₁₃⋊C₃	—	13	14	no	—
54	C₂×C₃²×C₅	—	169	1	no	—
55	C₃²×D₅	—	169	2	no	—
56	C₂×C₃×C₁₃	—	5	28	no	—
57	C₂×C₃×C₁₃	D₅×C₁₃⋊C₃	1	14	yes	complemented
58	C₂×C₁₃⋊C₃	—	13	42	no	—
59	C₂×C₁₃⋊C₃	—	65	84	no	—
60	C₅×C₁₃	C₂²×C₃×C₁₃⋊C₃	1	14	yes	complemented
61	C₂×C₃×D₅	—	169	3	no	—
62	C₂×C₃×D₅	#92788	1	1	yes	characteristic, direct product factor
63	C₂²×C₁₃	—	5	14	no	—
64	C₃²×C₅	—	169	1	no	Hall
65	C₃×C₁₃	C₂×D₅×C₁₃⋊C₃	1	14	yes	complemented
66	C₁₃⋊C₃	—	13	42	no	—
67	C₂²×C₃²	—	845	1	no	Hall
68	C₂×C₃×C₅	—	169	3	no	—
69	C₂×C₃×C₅	C₂×#92788	1	1	yes	characteristic, complemented
70	C₃×D₅	—	169	6	no	—
71	C₃×D₅	C₂×#92788	1	2	yes	direct product factor
72	C₂×C₁₃	—	5	28	no	—
73	C₂×C₁₃	C₃×D₅×C₁₃⋊C₃	1	14	yes	complemented
74	C₂×D₅	C₃×#92788	1	1	yes	characteristic, direct product factor, Hall
75	C₂×C₃²	—	845	2	no	—
76	C₂×C₃²	—	169	1	no	—
77	C₃×C₅	—	169	3	no	—
78	C₃×C₅	C₂²×#92788	1	1	yes	characteristic, complemented
79	C₁₃	C₂×C₃×D₅×C₁₃⋊C₃	1	14	yes	complemented
80	C₂²×C₃	—	5	1	no	—
81	C₂²×C₃	—	845	3	no	—
82	C₂×C₅	C₂×C₃×#92788	1	1	yes	characteristic, complemented
83	D₅	C₂×C₃×#92788	1	2	yes	direct product factor
84	C₃²	—	169	1	no	Sylow
85	C₂×C₃	—	5	2	no	—
86	C₂×C₃	—	845	6	no	—
87	C₂×C₃	—	169	3	no	—
88	C₂×C₃	D₅×#92788	1	1	yes	characteristic, direct product factor
89	C₅	C₂²×C₃×#92788	1	1	yes	characteristic, complemented, Sylow
90	C₂²	—	5	1	no	Sylow
91	C₃	—	169	3	no	—
92	C₃	C₂×D₅×#92788	1	1	yes	characteristic, direct product factor
93	C₂	—	5	2	no	—
94	C₂	C₃×D₅×#92788	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₅×#92788
commutator, cosocle, hypocenter	C₅×C₁₃²	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₃²	C₂×C₃
LCS	G ▷ C₅×C₁₃²
UCS	C₁ ◁ C₂×C₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃×C₅×#92788	C₂	semidirect
2. C₃×D₅×#92788	C₂	direct (N × H)
3. C₂×C₃×D₅×C₁₃²	C₃	semidirect
4. C₂×D₅×#92788	C₃	direct (N × H)
5. C₃×C₅×#92788	C₂²	semidirect
7. C₃×D₅×C₁₃²	C₂×C₃	semidirect
8. C₂×C₅×#92788	C₂×C₃	semidirect
9. D₅×#92788	C₂×C₃	direct (N × H)
10. C₂×C₃×C₅×C₁₃²	C₂×C₃	semidirect
11. C₂×D₅×C₁₃²	C₃²	semidirect
13. C₂×C₃×#92788	D₅	direct (N × H)
14. C₅×#92788	C₂²×C₃	semidirect
15. C₃×C₅×C₁₃²	C₂²×C₃	semidirect
19. C₂×C₅×C₁₃²	C₂×C₃²	semidirect
20. D₅×C₁₃²	C₂×C₃²	semidirect
21. C₃×#92788	C₂×D₅	direct (N × H)
25. C₂×C₃×C₁₃²	C₃×D₅	semidirect
27. C₂×#92788	C₃×D₅	direct (N × H)
28. C₅×C₁₃²	C₂²×C₃²	semidirect
29. C₂×C₃×D₅×C₁₃	C₁₃⋊C₃	semidirect
33. C₃×C₁₃²	C₂×C₃×D₅	semidirect
34. #92788	C₂×C₃×D₅	direct (N × H)
36. C₂×C₃×C₅×C₁₃	C₂×C₁₃⋊C₃	semidirect
37. C₃×D₅×C₁₃	C₂×C₁₃⋊C₃	semidirect
41. C₂×C₁₃²	C₃²×D₅	semidirect
42. C₂×D₅×C₁₃	C₃×C₁₃⋊C₃	semidirect
45. C₃×C₅×C₁₃	C₂²×C₁₃⋊C₃	semidirect
48. C₁₃²	C₂×C₃²×D₅	semidirect
51. C₂×C₅×C₁₃	C₂×C₃×C₁₃⋊C₃	semidirect
52. D₅×C₁₃	C₂×C₃×C₁₃⋊C₃	semidirect
57. C₂×C₃×C₁₃	D₅×C₁₃⋊C₃	semidirect
60. C₅×C₁₃	C₂²×C₃×C₁₃⋊C₃	semidirect
62. C₂×C₃×D₅	#92788	direct (N × H)
65. C₃×C₁₃	C₂×D₅×C₁₃⋊C₃	semidirect
69. C₂×C₃×C₅	C₂×#92788	semidirect
71. C₃×D₅	C₂×#92788	direct (N × H)
73. C₂×C₁₃	C₃×D₅×C₁₃⋊C₃	semidirect
74. C₂×D₅	C₃×#92788	direct (N × H)
78. C₃×C₅	C₂²×#92788	semidirect
79. C₁₃	C₂×C₃×D₅×C₁₃⋊C₃	semidirect
82. C₂×C₅	C₂×C₃×#92788	semidirect
83. D₅	C₂×C₃×#92788	direct (N × H)
88. C₂×C₃	D₅×#92788	direct (N × H)
89. C₅	C₂²×C₃×#92788	semidirect
92. C₃	C₂×D₅×#92788	direct (N × H)
94. C₂	C₃×D₅×#92788	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×#92788	2
C₃×D₅×#92788	2
C₂×C₃×D₅×C₁₃²	3
C₂×D₅×#92788	3
C₂²×C₃×#92788	5
C₂×C₃×D₅×C₁₃⋊C₃	13

Subgroups — C2×C3×D5×#92788 #44478159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₅×#92788 #44478159